Consider the geometric sequence . The explicit formula for the -th term of this sequence is . Find the value of and then determine . The value of is ________.
Answer & Analysis
Analysis
Question Analysis
This question tests the student's ability to identify the common ratio in a geometric sequence and use the explicit formula to find a specific term.
Key Concept Explanation
The key concept here is the explicit formula for the -th term of a geometric sequence, (), where is the first term and is the common ratio.
Step-by-step Solution
1. Identify the first term .
2. Calculate the common ratio using the second term:
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